The solutions of dissipation-dispersive models arising in material science

Abstract

Purpose The aim of this work is to obtain periodic waves of Eq. (1) via ansatz-based methods. So, the open questions are replied and the gap will be filled in the literature. Additionally, the comparison of the considered models (Eq. (1) and Eq. (2)) due to their performance. Although it is extremely difficult to find the exact wave solutions in Eq. (1) and Eq. (2) without any assumptions, the targeted solutions have been obtained with the chosen method. Design/methodology/approach Material science is the today's popular research area. So, the well-known model is the dissipation double dispersive nonlinear equation and, in the literature, open queries have been seen. The aim of this work is to reply open queries by obtaining wave solutions of the dissipation double dispersive model, double dispersive model and double dispersive model for Murnaghan's material via ansatz-based methods. Findings The results have been appeared for the first time in this communication work and they may be valuable for developing uses in material science. Originality/value The exact wave solutions of Eq. (1) and Eq. (2) without any assumptions have been obtained with via ansatz-based method. So, the open questions are replied and the gap will be filled in the literature.